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# The product of the units digit, the tens digit, and the

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VP
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The product of the units digit, the tens digit, and the [#permalink]  12 Jan 2008, 03:21
The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m?

(1) m is odd.
(2) The hundreds digit of m is 8
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Re: some digits [#permalink]  12 Jan 2008, 06:21
it is C.
the number is 843.

statement1, although useful still insufficient. the only odd factor in 96 is 3. so if units digit is 3, the product of the first two ones must be 32 (32*3=96).

statement2 says hundreds is 8. alone is insuff

but both statements are suff. 843
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Re: some digits [#permalink]  12 Jan 2008, 07:14
CaspAreaGuy wrote:
it is C.
the number is 843.

statement1, although useful still insufficient. the only odd factor in 96 is 3. so if units digit is 3, the product of the first two ones must be 32 (32*3=96).

statement2 says hundreds is 8. alone is insuff

but both statements are suff. 843

OA is A

if m is odd, then the unit digit is 3, since 96= 2^5 *3. any other combination would give us an even number
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Re: some digits [#permalink]  12 Jan 2008, 11:03
marcodonzelli wrote:
The product of the units digit, the tens digit, and the hundreds digit of the positive integer m is 96. What is the units digit of m?

(1) m is odd.
(2) The hundreds digit of m is 8

1. prime factors m=xyz
96-2
48-2
24-2
12-2

6-2
3-3
1-1

so: hundreds and tens digits can be either 8 or 2 then units digit has to be 3.

suff.

2. m=xyz then y=8, then x and z can either be 4 or 3 so we cannot say anything from this statement. insuff.

A for me.
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Re: some digits [#permalink]  12 Jan 2008, 15:40
1
KUDOS
Agree with Marco. A.

2^5X3, You can't have 2 (or any of its multiples e.g. 4, 8, etc) as Units digit, otherwise it will be even.
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Re: some digits [#permalink]  08 Nov 2011, 12:00
1
KUDOS
96 = 2^5 * 3

1) m is odd
so units digit can be 1 or 3 based on the factors. but it cannot be 1 as no two single digits integers can give a product of 96.
So units digit is 3 - SUFFICIENT

2) hundreds digit is 8
Insufficient as number could be 843 or 826 or 834 or 862

Ans: A
Re: some digits   [#permalink] 08 Nov 2011, 12:00
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